Keywords: moving load, finite element method, quasi-stationary dynamic response, transient dynamic response, absorbing boundary conditions, plastic deformation.

Railway transportation is in the process of creating new lines, updating existing ones and increasing the capacity of the whole network. This brings new issues related to the dynamic response of railway tracks to moving loads. Computational tools capable of providing quick and accurate response to the arising questions are needed.

Simplified models of railway tracks are widely used because they provide quick and simple replies to some fundamental issues, among other advantages [1,2]. However, when nonlinear effects such as irreversible ballast settlements are important, a complete model involving all structural details is preferable. Solving them using the finite element (FE) method, presents some difficult choices: (i) the size of the model, (ii) the size of the finite elements and (iii) the type of boundary conditions.

In this contribution new techniques for solving induced vibrations from moving loads by finite element software are proposed. These techniques allows for significant computation time reduction. The enhanced moving window method (EMWM) functions on a relatively small model, from which using an iteration procedure either a quasi-stationary solution that would be developed on an infinite structure, or a response of the structure encompassing transitions, can be obtained. The EMWM can be generalized to account for periodically distributed inhomogeneities in the longitudinal direction. It is also valid in the geometrically nonlinear range and reversible physically nonlinearity range if the same loading and unloading paths are followed. In the linear case a set of loads can be modelled by superposition. Implementation of a set of loads in the nonlinear case and an irreversible physical nonlinearity (plasticity), is solved by time-dependent boundary conditions (T-DB). The main advantages are: (i) the model itself can be rather small, but the time dependent results can cover an arbitrarily large model; (ii) nonlinearities can be introduced; (iii) transitions can be accounted for; (iv) calculation time is acceptable.

The EMWM and its extension by the T-DB are implemented in the ANSYS software [3]. Numerical procedures are automated using the ANSYS Parametric Design Language. Several case studies and the influence of various parameters are investigated, comparing results with analytical solutions and long simulations on large models. Accuracy is verified by comparison with analytical solutions and results from the long simulation on a large model using the L²-norm.

1

Z. Dimitrovová, J.N. Varandas, "Critical velocity of a load moving on a beam with a sudden change of foundation stiffness: applications to high-speed trains", Computers & Structures, 87, 1224-1232, 2009. doi:10.1016/j.compstruc.2008.12.005

2

Z. Dimitrovová, "A general procedure for the dynamic analysis of finite and infinite beams on piece-wise homogeneous foundation under moving loads", Journal of Sound and Vibration, 329, 2635-2653, 2010. doi:10.1016/j.jsv.2010.01.017

3

ANSYS, Inc. Documentation for Release 12.1, Swanson Analysis Systems IP, Inc., November 2009.

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